Concept explainers
Finding a Limit Using Spherical Coordinates In Exercises 77 and 78, use spherical coordinates to find the limit.[ Hint: Let
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Calculus: Early Transcendental Functions
- Limits at infinity Determine the following limits. cos u lim uSo u?arrow_forward(a) Show that the limit does not exist by considering the limits as (x, y) →(0,0) along the coordinate axes. x+y lim (x,y) 700) 2xy (b) Evaluate the limit by converting to polar coordinates. lim (x)-(0,0) In (x² + y²)arrow_forwardUse polar coordinates to find the limit. [If (r, ?) are polar coordinates of the point (x, y) with r ≥ 0, note that r → 0+ as (x, y) → (0, 0).] (If an answer does not exist, enter DNE.) lim (x, y)→(0, 0) (x2 + y2) ln(x2 + y2)arrow_forward
- secy-1 Lim sec2y-1 a) as y → 0 b) as y → n/2arrow_forwardUsing Green's theorem find the value of f F.drWhere F(x,y) = (e* – y³)i + (cosy + x³)j and C is the closed triangle bounded by the lines x = 0, y = 0 and x + y = 2.arrow_forwardEvaluate the limit or show that it DNE. lim (x,y)-(0,0) (x- y²)(y-x²) x4 + y4 +arrow_forward
- Question 1 4xy f(x, y) = 2x²+5² a)!* s Find the domain of f. b) [₁ Show that the limit Consider the function does not exist. lim f(x, y) (x,y)→(0,0)arrow_forwardEvaluating limits: Evaluate the following limits, or explain whythe limit does not exist. lim(x,y)→(1,2)x2 + y2/x2 − y2 lim(x,y)→(4,π)tan−1( y/x)arrow_forward|sin z| Lim z0 sin zarrow_forward
- Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate that using the check box. sin(x² + y? + z²) lim (x,y,z)→(0,0,0) Does not exist Vx2 + y? + z²arrow_forward(i) Evaluate the limit or show that it does not exist. 2xy lim (x,y) →(0,0) x² + 2y² дz (ii) If cos(xyz) = 1 + x²y² + z², find 3ž and дуarrow_forwardUse polar coordinates to find the limit. [If (r, 0) are polar coordinates of the point (x, y) with r2 0, note that r- 0+ as (x, y) → (0, 0).] (If an answer does not exist, enter DNE.) 4e-x2 - y? - 4 x² + y2 lim (x, y)- (0, 0)arrow_forward
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